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Results tagged with eigenvalues
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user 64692
eigenvalues of matrices or operators
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Determinant of the sum of a psd (Kronecker) matrix and a diagonal matrix?
My current approach:
$$det(KW + I) = det((K + W^{-1})W) = det(K+W^{-1})det(W)$$
Let $a_i$ be the eigenvalues of $K$ and $b_i$ be the eigenvalues of $W^{-1}$ sorted $a_1 \geq a_2 \geq \ldots \geq a_N … $\dagger$ Let $e_i$ be the $n$ eigenvalues of $K_1$ and $f_j$ be the $m$ eigenvalues of $K_2$. Then $det(K1 \otimes K2) = \prod_{ij} (e_i)^m (e_j)^n$. …
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